Resonant frequency

The resonant frequency is the frequency at which the amplitude of a vibratory system is greater than the excitation frequencies by adjacent. Partial is meant by the resonance frequency, the frequency at which the output of a phase angle of 90 ° to the excitation has ( phase resonance). This is the case with the undamped natural frequency. For weakly damped systems this difference is small. Depending on the number of degrees of freedom of the system, there are also a plurality of resonance frequencies.

Properties

The vibration system is excited near the resonant frequency, as occur with little attenuation to large amplitudes. This is often undesirable, such as in buildings, cable car cabins, overhead power lines etc. and can lead to disaster response. To avoid damaging vibration absorber be installed. In electrical resonant circuits, or for acoustic sound generation of the effect is sometimes desirable when the amplitude is to be increased. For speakers, however, no possible resonance frequencies will occur, as this some tones are very loud. With increasing deviation of the excitation frequency reduces the amplitude.

In the vicinity of the resonance frequency, the phase between exciting and excited vibrational changes particularly strong.

Examples of undamped systems

Resonance frequencies occur in systems with at least two different types of energy storage. In simple ( theoretical ) systems without damping, the resonance frequency is equal to the undamped natural frequency ( frequency characteristics ). When the frequency is damped systems in which the maximum amplitude occurs is always lower than the undamped natural frequency.

• In a resonant circuit, the oscillation Thomson equation

Where L is the inductance of the coil, and C represent the capacitance of the capacitor. Here, the field energy of the capacitor converts periodically to the magnetic energy of the coil.

• A spring hardness D and a weight from m form a mechanical vibration system to the natural frequency

• A pendulum of length leads under the influence of gravity oscillations at the frequency

From.

• Ground and the ionosphere, both electrically well conductive, define a spherical cavity, the Schumann resonances can be calculated:

Where n = 1, 2, 3 ... is - there are multiple resonances. c is the speed of light and a is the Earth's circumference.

• A laser resonator of length L usually has very many, closely spaced resonant frequencies

Quantum mechanical systems

Quantum mechanical systems, while only limited classical vibration systems. However, one also speaks here of resonance frequencies. In contrast to classical oscillatory systems interactions can take place only at the respective resonant frequencies. At the same time, each frequency corresponding to such a system, a specific energy of a particle, and so that each resonance frequency then a so-called resonance energy. The fact that each spread as propagation of a wave can be described, but each interaction as an interaction of particles, wave -particle duality is called.

Light, for example, spread in the form of electromagnetic waves. Interactions such as absorption and emission take place in the form of photons. In this case, each photon corresponds to a specific frequency by the amount of radiant energy. When a photon is absorbed or emitted by an electron of an atom, it is said, the photon (or electromagnetic field) and the electron are in resonance. In a spectrum formed at the corresponding frequency spectrum line.